1.5. Fluid Deformation Between Parallel Plates

So, we will see an example, where fluid deformation between parallel plates is done. So, this is the side view, where a force F is applied and the upper plate starts moving with velocity U and the thickness of the…the total thickness is given here denoted as t.

Fluids can deform easily when a force is applied. In this example, imagine two parallel plates with a fluid in between. When a force (F) is applied to one plate, it pushes against the fluid, causing the upper plate to move at a certain velocity (U). The thickness of the fluid layer between the plates is denoted as 't'. This situation helps us understand how fluids behave when subjected to forces.

Think of this setup like a stack of playing cards. If you push the top card, it slides over the others beneath it. The force you apply is similar to the force (F) that causes the upper plate to move.

Now, what are the parameters can control how much force is required to get a desired velocity, as has been seen from the experiment, distance between the plates which is denoted as t is quite an important parameter. Area of the plate A is also very important parameter viscosity is also important parameter.

Several parameters influence how much force is required to achieve a specific velocity of the moving plate: 1. Distance between the plates (t): A smaller distance allows the fluid to move more easily. 2. Area of the plate (A): Bigger plate areas require more force due to the larger surface interacting with the fluid. 3. Viscosity: This measures the fluid's resistance to flow; thicker fluids (high viscosity) require more force to move.

Imagine trying to slide a broad book on a smooth table versus a thick, heavy book. The thicker book (high viscosity) resists movement more than the smooth book (low viscosity).

So, F is found out to be directly proportional to area speed, but inversely proportional to the distance between the plates.

The relationship between force (F), area (A), velocity (U), and the distance between the plates (t) is important: - The force increases with a larger plate area or a higher velocity (U). - However, increasing the distance (t) between the plates makes it harder for the fluid to flow, meaning the force needed increases. Thus, F ∝ (A * U) / t.

Consider squeezing a thick tube of toothpaste. If the tube is wider (more area), it pushes out more toothpaste quickly (higher velocity) with less effort. However, if the tube is longer (greater distance), you have to apply more force to get the same amount of toothpaste out.

Shear stress is defined as (Force / Area) and its dimension is N/m² or units is N/m². Shear stress can be written as (μ * (U / t)).

Shear stress describes how much force the fluid layers exert against each other when they move. It is determined by dividing the force applied (F) by the area (A) that the force acts upon. The formula also shows shear stress relates to the fluid's viscosity (μ) and the change in velocity over the thickness of the fluid layer (U/t).

You can visualize shear stress like the pressure on a platter when you stack multiple plates. Each plate's weight and the area pressing down create stress, similar to how the fluid layers interact under shear conditions.

Some examples of highly viscous fluids are molasses, tar, oil, etc. The fundamental mechanism of viscosity in gases is due to the transfer of the molecular momentum.

Viscosity measures a fluid's resistance to flow. For example, sticky liquids like molasses or tar have high viscosity, making them flow slowly. In gases, viscosity is mainly caused by how rapidly gas molecules transfer momentum when they collide with each other. The higher the temperature, the more molecules move around, which changes viscosity.

Think of honey compared to water. When you pour honey, it flows slowly and takes time to move (high viscosity), whereas water flows quickly (low viscosity). This difference is due to their unique molecular structures and viscosity.

One of the examples that we will talk about is used to measure the viscosity of the water. It is a very standard experiment...

In this example, an experiment is conducted using a rotating cylinder between stationary ones. The viscosity of water can be calculated based on the power required to rotate the inner cylinder at a specific speed. The relationship between the fluid's motion and the applied force allows us to derive its viscosity quantitatively.

Consider a blender mixing thick batter vs. a smoothie. The battery's viscosity causes the blades to work harder (more power needed) compared to a smoothie, which mixes easily due to lower viscosity. This illustrates how viscosity impacts mechanical effort.

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